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The potential ambiguity is forestalled by context - if the headline writer is competent.
Meaning derives from context in general, and the context of a headline (which is not embedded in other text) is the surrounding circumstances.
Entire websites chronicle what can happen when a headline/billboard/slogan/bumper sticker writer overlooks the context of the reader.

An example of the challenges facing machine translation.

In some circumstances involving an article presumably written by a non-American, "2" might be default. Imagine a subheading in smaller type, in an article written by an Australian emigrant and appearing in their hometown newspaper, that reads "but they might not like you".

This was the headline of an article in NY Times Feb. 11. When I looked at it, before reading the article, I realized it had two completely different possible interpretations.

(1) Americans who are like me.
(2) Americans who do like me.

Is this ambiguity unavoidable? It turns out the article was about (1).

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Yes, semantic ambiguity in natural language is unavoidable.

There's a standard example in the theory of natural language processing. We'd like to be able to parse a sentence mechanically. Here's the subject, here's the verb form, here's the object. But that doesn't work. The example is,

Time flies like an arrow.

Fruit flies like a banana.

In the first sentence, the subject is "time," the verb is "flies," and then there's a comparison via "like." Easy to parse.

But in the second example, the subject is "Fruit flies." How would a program know that? It has to know that fruit flies are a type of insect attracted to fruit, and that therefore they would "like" a banana. In this case like is not the start of a comparison of two things; rather, it's the verb! And "fruit flies" must be read as one single thing, rather than a subject and a verb.

How could a syntax parser ever figure this out? The answer is that it can't. This is one reason Google translate is so bad. Natural language processing is a very difficult problem for computers. But an easy one for human toddlers. Let the computationalists explain that!

The article immediately followed the headline. Reading it resolved the ambiguity.

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The subsequent small print is not the context of a headline when first read. The initial meaning of a headline derives from the context of its reading and reader - the publication it's in, recent events, the larger world.

Less. In fact, wrong altogether.
The difficulties of the absent context of text - rendering clear subordinate clauses almost impossible, for example, since the "ordinate" is missing - make commas vanishingly rare in headlines.

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ok, but was it clearer that the author was an American?
Dutchmen, like me, don't use the word ordinate. Can you define "ordinate" for me?